Piezoelectric Cylindrical Shell Research Articles

Electroelastic effects on local-global buckling of piezoelectric cylindrical shells with stepped thickness

Electroelastic effects on local-global buckling of piezoelectric cylindrical shells with stepped thickness

Buckling Analysis of Composite Piezoelectric Cylindrical Shells with Graphene Skin Subjected to the Axial Load

The buckling of new three‐phase composite shells, which include the base material combined with macro fiber composite and reinforced with graphene (MFC‐GP), is investigated in this article. The bifurcation condition of the buckling is obtained by implementing the first‐order shell theory and wave propagation theory in conjunction with the principle of minimum potential energy. The buckling analysis is transformed into a bifurcation problem of equations. Parametric study is conducted to investigate the effects of the GP volume fraction, length, neutral surface radius, and thickness on the critical buckling loads and critical buckling modes. Furthermore, the influences of voltage and temperature change on the critical buckling displacements are explored. Reliable theoretical support for the design and manufacture of the MFC‐GP structures is provided in the results.

Porosity and size effects on electro-hygrothermal bending of FG sandwich piezoelectric cylindrical shells with porous core via a four-variable shell theory

The sinusoidal four-variable shear deformation shell theory is employed, for the first time, to investigate the size dependent electro-hygrothermal bending of functionally graded (FG) sandwich piezoelectric cylindrical shells integrated with porous core. This model is assumed to be rested on two-parameter elastic foundations and subjected to elevated temperature, moisture concentration and external electric voltage as well as transverse mechanical loads. In order to take into account the size effect, the modified couple stress theory is employed containing only one length scale parameter. The core layer is assumed to be functionally graded porous material. Whereas, the face sheets are made of a functionally graded piezoelectric material which having gradient change along the thickness direction. Based on the sinusoidal four-variable shell theory, four governing equations are obtained involving external forces and foundation interaction, in addition to an equation associated to the electrical potential. An analytical solution for the obtained equations is presented to get the displacements and stresses of the FG sandwich piezoelectric cylindrical shells. Influences of the geometric parameters, material length scale parameter, temperature rise, moisture concentration, electric voltage, porosity factor, core thickness and foundation coefficients on the bending of the FG sandwich piezoelectric cylindrical shells resting on elastic foundations are discussed.

Free vibration characteristics of piezoelectric cylindrical shells with stepped thickness using an analytical symplectic approach

An analytical study on free vibration of stepped-thickness piezoelectric cylindrical shells is performed under the framework of symplectic mechanics. In the proposed symplectic approach, the step-wise thickness in the axial direction is considered by regarding the overall shell as a combination of multiple segments with different uniform thicknesses. The Hamiltonian governing equations for free vibration of each segment are established by defining a new total unknown vector and the Reissner's thin shell theory. In this manner, analytical solutions can be represented by a series of symplectic eigenfunctions with undetermined coefficients. By using boundary conditions at the ends and interfaces, the coefficients of symplectic series are easily obtained by solving a set of algebraic equations. Consequently, the natural frequencies and analytical mode shapes are obtained simultaneously. The methodology is rational and rigorous, and the solution procedure is systematic with a step-by-step definition. Numerical results are compared with those reported in the open literature and good agreements are observed. A comprehensive parametric study of stepped thickness on vibration characteristics of piezoelectric cylindrical shells are carried out also. The results demonstrate that the local thickness thinning will decrease natural frequencies and lead to local deformation modes. Some of them can be served as benchmarks for other numerical or approximate methods.

A boundary layer solution for the post-critical thermo-electro-mechanical stability of nonlocal-strain gradient Functionally Graded Piezoelectric cylindrical shells

Continuum mechanics is extended to the Nonlocal (NL) and the Strain Gradient (SG) theories by incorporating the long-range molecular interactions. Nanostructures are often made of smart materials (e.g. Piezoelectric) for multifunctional attributes. The NL-SG theory based analysis/design of nanostructures offers convenience comparing the computationally expensive atomistic simulation. This study investigates the thermal post-buckling of a piezoelectric, NLSG thin cylindrical shell with thickness-wise gradation of elastic properties. The governing equations are derived following the Donnell's approach including the pre-buckling nonlinearity, large post-critical deflection and geometric imperfections. A thickness-wise cosine distribution of the electric potential is employed following the Maxwell equation. The Boundary Layer (BL) concept is employed to solve the nonlinear equations using asymptotic expansions of the regular and the BL field variables. The solution is illustrated on moderately short shells to show the prominent SG but nominal NL effects. The interactions result in conservative critical temperature but non-conservative post-critical path in contrast with the classical shell. The influence of functional gradation and the electric fields are illustrated. Increasingly sharper displacement gradient around the BL of the SG shell suggests the increasing relevance of the BL theory. The proposed solution may be useful for analysis, design and active instability control by adaptive feedback voltage.

Vibration and acoustic radiation characteristics of cylindrical piezoelectric transducers with circumferential steps

Circular cylindrical transducers have a wide range of applications in ultrasound generation. Introducing axial or circumferential stepped-thickness variations affects the performance of these transducers. This paper investigates the effect of circumferential stepped-thickness variations on the vibration and acoustic characteristics of a circular cylindrical piezoelectric shell. FEM software ANSYS is used to simulate these characteristics and experiments are performed to validate the simulations. Stress concentration levels due to these steps are observed in order to avoid exceeding the material limit. The results show that these steps can excite certain mode shapes which produce strong ultrasound fields and these modes have circumferential wave numbers commensurate with the number of stepped regions. These steps localize the vibration within the thin-walled regions leading to higher amplitude acoustic waves produced by constructive interference. Superiority of a circumferentially stepped transducer over an axially stepped one is demonstrated in this study through a much more uniform acoustic field along the length of the transducer as well as a lower frequency of operation at the intended mode shape. The effect of input excitation is also investigated and it is shown that introducing circumferential steps is more effective in terms of acoustic amplification than increasing the input excitation for the uniform-thickness transducer.

Dynamic instability zone analysis of laminated piezoelectric cylindrical shell with delamination under hygrothermal effects

To use effectively the shell in high-performance applications, analyzing the effect of hygrothermal effects on a piezoelectric delamination event is necessary. A laminated piezoelectric cylindrical shell with delamination is first established under hygrothermal effects, followed by an internal force analysis and an energy analysis of the shell. Then, a parametric vibration equation of the Mathieu for the shell is obtained by using the energy variation of the Rayleigh-Ritz method; later on, the harmonic balance method is employed to solve this equation. Finally, the effects of delamination parameters, geometric parameters, hygrothermal effects, and piezoelectric materials on the shell under uniformly distributed axial load are discussed.

Electro-thermo-mechanical post-buckling of piezoelectric functionally graded cylindrical shells

Unlike the widely used eigen-buckling theory, the nonlinear post-buckling analysis provides a more accurate stability model of piezoelectric cylindrical shells and predicates more reliable instability characteristics. In this paper, an accurate post-buckling analysis of piezoelectric functionally graded cylindrical shells under combined electro-thermo-mechanical loadings is performed. The nonlinear large deflection governing equations involving the self-induced electric potential are established based on the higher-order shear deformation theory. The post-buckling equilibrium paths with mode-jumping phenomenon for both symmetric and asymmetric deformation modes are obtained by the Galerkin's method enriched with new displacement functions. Results indicate that the symmetric mode usually occurs for a thick shell and the asymmetric mode only occurs for an ultrathin shell. Furthermore, it is demonstrated that the effect of power law index highly depends on the external electro-thermal loadings. Therefore, the loading capacity of the piezoelectric FG cylindrical shells can be improved by an appropriately selected power law index.

Nonlinear forced vibrations of functionally graded piezoelectric cylindrical shells under electric-thermo-mechanical loads

This paper develops a new solution approach to solve nonlinear forced vibrations of functionally graded (FG) piezoelectric shells in multi-physics fields. The FG piezoelectric shells are subjected to electric-thermo-mechanical loads, and the effect of micro-voids is considered here. Motion equations are obtained by using Hamilton's principle, and combining with the Donnell nonlinear shallow shell theory. Afterwards, a new method combining multi-mode Galerkin scheme and Pseudo-arclength continuation method is used to solve the nonlinear multiple internal resonances and bifurcations of the multi-degree-of-freedom systems. The novel feature of this approach is that it can efficiently obtain the unstable solution and tackle the difficult problems in mathematics encountered during formulation. The results show that the external applied voltage, temperature change, external excitation, power-law exponent, and porosity volume fraction play important roles on nonlinear vibration response and bifurcation analysis of FG piezoelectric shells with micro-voids.

Nonlinear Dynamic Analysis and Control of FG Cylindrical Shell Fitted with Piezoelectric Layers

In this study, the nonlinear vibration control of functionally graded laminated piezoelectric cylindrical shells under simultaneous parametric axial and radial external excitations is presented. The partial differential equations of shells are derived based on Hamilton’s principle, first-order shear deformation theory (FSDT), and nonlinear von Karman relations. The coupled nonlinear ordinary differential equations are obtained by Galerkin’s procedure and solved by the method of static condensation. Two piezoelectric layers are placed on the outer and inner surfaces of the cylindrical shell each as distributed sensor and actuator. Then the constant-gain negative velocity feedback strategy is employed. Regarding the nonlinear equations of motion, for the first time, the vibration analysis and active vibration control of smart FG cylindrical shells under combined parametric and external excitations are analyzed using the multiple scales approach. The effects of various parameters such as power index, external excitation’s amplitude, and control gain on the dynamic behavior of the system are investigated, using bifurcation diagrams, phase portraits, time histories, and Poincare maps. It is shown that quasi-periodic motion is the most common behavior of the system and controller gain and power index have inevitable effects on enhancing the quasi-periodic response of the system. Care should be exerted in selecting the parameters to have the desired response in the broad range of excitation frequency.

Non-Linear Response of Torsional Buckling Piezoelectric Cylindrical Shell Reinforced with DWBNNTs Under Combination of Electro-Thermo-Mechanical Loadings in Elastic Foundation

Nanocomposites provide new properties and exploit unique synergism between materials. Polyvinylidene fluoride (PVDF) is an ideal piezoelectric matrix applicable in nanocomposites in a broad range of industries from oil and gas to electronics and automotive. And boron nitride nanotubes (BNNTs) show high mechanical, electrical and chemical properties. In this paper, the critical torsional load of a composite tube made of PVDF reinforced with double-walled BNNTs is investigated, under a combination of electro-thermo-mechanical loading. First, a nanocomposite smart tube is modeled as an isotropic cylindrical shell in an elastic foundation. Next, employing the classical shell theory, strain-displacement equations are derived so loads and moments are obtained. Then, the total energy equation is determined, consisting of strain energy of shell, energy due to external work, and energy due to elastic foundation. Additionally, equilibrium equations are derived in cylindrical coordinates as triply orthogonal, utilizing Euler equations; subsequently, stability equations are developed through the equivalent method in adjacent points. The developed equations are solved using the wave technique to achieve critical torsional torque. Results indicated that critical torsional buckling load occurred in axial half-wave number m = 24 and circumferential wave number n = 1, for the investigated cylindrical shell. The results also showed that with the increase in the length-to-radius ratio and in the radius-to-shell thickness ratio, the critical torsional buckling load increased and decreased, respectively. Lastly, results are compared in various states through a numerical method. Moreover, stability equations are validated via comparison with the shell and sheet equations in the literature.

Deformation of laminated and sandwich cylindrical shell with covered or embedded piezoelectric layers under compression and electrical loading

A three-dimensional (3D) theory of elasticity is presented for the solution of the generalized displacements and stresses in the composite laminated and sandwich cylindrical shell structures with covered or embedded piezoelectric layers based on the scaled boundary finite element method (SBFEM). The SBFEM is a weak-form differential technique, which can lead to accurate results performing discretization only on the middle plane of shell structures so that the considered model can be treated as a two-dimensional (2D) discretizated problem. A new type 2D high order spectral element shape function is introduced both for approximations of geometry model and basis variables in the scaled boundary coordinate system. Employing the weighted residual principle in conjunction with Green’s theorem to the normalized static equilibrium equations of each layer leads to the SBFEM governing equation with respect to the radial generalized displacement fields. Then a system of a first-order ordinary differential equation is obtained by introducing a dual variable and analytically solved by using the precise integration technique (PIT). As a result, the major advantage of the proposed formulations for solving the bending problem of the composite laminated and sandwich cylindrical piezoelectric shell is no need to discretize the 3D model with a great deal of degrees of freedom while ensures the computational accuracy. Two test examples are carried out to demonstrate the adaptability and reliability of the present method and illustrate very good agreements and rapid convergence with the solutions based on the finite element approach only using a small number of elements. Numerical examples about the sandwich cylindrical piezoelectric shell are presented to investigate the parametric effects of the thickness ratio as well as the stacking sequence on the variation of generalized displacements and stresses. The results show that both the thickness ratio and stacking sequence have significant influence on the bending behaviors of the sandwich cylindrical piezoelectric shells.

Dynamic analysis of laminated piezoelectric cylindrical shells

The method of reverberation-ray matrix (MRRM) has been successfully utilized to study the transient waves in beams, plates and laminated solids. In this work, the MRRM is adopted to study the transient responses and wave propagation of piezoelectric cylindrical shells with finite size. Based on the Donnell shell theory, the reverberation matrix formulation in the cylindrical shell is derived. Using Laplace transformation, the transient responses under imposed impact load can be predicted. Through the numerical simulations, the early short time transient responses can be further elucidated. Furthermore, the effects of the geometric parameters of the composite shells on the wave propagating in the laminated piezoelectric shells are also analyzed.

Vibration of circumferentially stepped-thickness piezoelectric cylindrical shells

In this work, thickness variations are introduced around the circumference of a piezoelectric cylindrical shell. The aim is to investigate the vibration characteristics of the shells and the effect of these step-thickness variations on the mode shape of vibration. These thickness variations require stress distribution analysis as well to avoid failure of the cylindrical shell. To this aim, two configurations of stepped-thickness shells with two and three circumferential thickness variations are investigated using FEA software, ANSYS. The results show that these steps assist in localizing vibration in the thin sections and excite mode shapes having the same circumferential wave number as the number of thickness variations. This can be a suitable approach to control and forcibly excite certain vibration mode shapes, which might be required for some applications.

Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells

Each guided elastic wave mode is composed of propagating and non-propagating branches. Non-propagating branches associated with complex wavenumbers are substantially different from the propagating ...

Exact thermoelectroelastic solution of layered one-dimensional quasicrystal cylindrical shells

Laminated shells have been widely used as intelligent structures in many industries due to their unique characteristics of high strength/weight and stiffness/weight ratios. This paper presents a thermoelectromechanical analysis of multilayered one-dimensional piezoelectric quasicrystal cylindrical shells under surface heating, which are simply supported at circumferential edges and infinitely at axial direction. The exact solution is obtained based on the extended pseudo-Stroh formalism and a dual variable and position method with good computational stability, and it is utilized to study the effects of shell curvature, loading condition and stacking sequence on phonon, phason, thermal and electric fields.

Wave propagation in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented carbon nanotubes

Wave propagation behavior in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented, straight carbon nanotubes (CNTs) is analytically investigated for the first time via the first-order shear deformation shell theory including the transverse shear effects and rotary inertia. The Mori-Tanaka method is used for micromechanical modeling. Dispersion solutions are computed by solving an eigenvalue problem. The effects of CNT orientation, CNT volume fraction, and shell geometry on the dispersion solutions are examined. Various orientations of CNTs lead to different dispersion behaviors; the variation of wave phase velocities is more significant at lower axial wave numbers; and the effects of CNT volume fraction and shell geometry on wave dispersion behaviors are more obvious at higher circumferential wave numbers. The presented model and analytical results of this study can be utilized in the wave propagation analysis of piezoelectric shells reinforced with CNTs for the design of new smart structures used in structural health monitoring and/or energy harvesting applications.

Acoustic amplification utilizing stepped-thickness piezoelectric circular cylindrical shells

This paper presents a new approach to amplify the acoustic field generated by a uniform thickness piezoelectric cylindrical shell by introducing a stepped thickness variation at predetermined axial locations. The acoustic field and corresponding mode shapes of a uniform thickness piezoelectric tube are analyzed first and then, axial thickness variations are machined within the specified designed regions of the tube. The machining leads to the formation of thin-walled regions in the tube which localize the vibration amplitude within the machined spaces with higher amplitude. This results in a conspicuous increase of approximately 85% on average in the strength of the resultant acoustic field, though both specimens the uniform and stepped-thickness tubes have the same power consumption. The results of the simulations and experiments are in good agreement.

Buckling and free vibration analysis of high speed rotating carbon nanotube reinforced cylindrical piezoelectric shell

• Buckling and vibration behavior of a piezoelectric rotating (CNTRC) shell is investigated. • The generalized differential quadrature method is employed to solve the governing equations. • Both cases of uniform distribution and FG distribution patterns of reinforcements are studied. • Effect of various parameters on critical voltage and natural frequency of piezoelectric rotating CNTRC shell is investigated. In this paper, buckling and free vibration behavior of a piezoelectric rotating cylindrical carbon nanotube-reinforced (CNTRC) shell is investigated. Both cases of uniform distribution (UD) and FG distribution patterns of reinforcements are studied. The accuracy of the presented model is verified with previous studies and also with those obtained by Navier analytical method. The novelty of this study is investigating the effects of critical voltage and CNT reinforcement as well as satisfying various boundary conditions implemented on the piezoelectric rotating cylindrical CNTRC shell. The governing equations and boundary conditions have been developed using Hamilton's principle and are solved with the aid of Navier and generalized differential quadrature (GDQ) methods. In this research, the buckling phenomena in the piezoelectric rotating cylindrical CNTRC shell occur as the natural frequency is equal to zero. The results show that, various types of CNT reinforcement, length to radius ratio, external voltage, angular velocity, initial hoop tension and boundary conditions play important roles on critical voltage and natural frequency of piezoelectric rotating cylindrical CNTRC shell.

Analysis of wave propagation characteristics in piezoelectric cylindrical composite shells reinforced with carbon nanotubes

Wave propagation is studied and analyzed in a piezoelectric cylindrical composite shell reinforced with carbon nanotubes (CNTs) by using the Mori-Tanaka micromechanical model and considering the transverse shear effects and rotary inertia via the first-order shear deformation shell theory for the first time. The novelty of this study is to provide a mathematical model and solution to investigate the wave behavior in a CNT-reinforced piezoelectric cylindrical composite shell by considering the transverse shear effects and rotary inertia. Dispersion solutions are obtained by solving an eigenvalue problem. The effects of axial and circumferential wave numbers on dispersion curves are explained. The effects of carbon nanotubes and shell geometry parameters on dispersion solutions are examined as well. In addition, a comparison of dispersion solutions from different shell theories within different axial and circumferential wave numbers and CNT volume fractions is provided to illustrate the transverse shear and rotary inertia effects on wave propagation characteristics. The results of this paper can be used for studies on wave propagation in piezoelectric composite shell structures and in design of smart composite shell structures with piezoelectric materials for dynamic stability analysis and structural health monitoring.